Refraction of Light: Understanding Snell’s Law and Applications
What Is Refraction?
Refraction occurs when light changes direction as it passes from one medium to another due to a change in its speed.
Snell’s Law
The relationship between the angles of incidence and refraction is given by:
\[
n_1 \sin\theta_1 = n_2 \sin\theta_2
\]
Where:
- \( n_1, n_2 \): Refractive indices of the two media.
- \( \theta_1, \theta_2 \): Angles of incidence and refraction.
Refractive Index (\( n \))
The refractive index measures how much a medium slows down light:
\[
n = \frac{c}{v}
\]
Where:
- \( c \): Speed of light in a vacuum (\( 3.0 \times 10^8 \, \text{m/s} \)).
- \( v \): Speed of light in the medium.
Applications of Refraction
Lenses
Refraction focuses light to form images in cameras and microscopes.
Fiber Optics
Light is guided through optical fibers using total internal reflection.
Atmospheric Science
Refraction creates phenomena like mirages and rainbows.
Example Problem
A light ray enters water (\( n = 1.33 \)) from air (\( n = 1.00 \)) at an angle of \( 30^\circ \). Find the angle of refraction.
- Formula:
\[
\sin\theta_2 = \frac{n_1 \sin\theta_1}{n_2}
\]
- Substitute Values:
\[
\sin\theta_2 = \frac{1.00 \cdot \sin 30^\circ}{1.33} = \frac{0.5}{1.33} \approx 0.376
\]
- Result:
\[
\theta_2 = \sin^{-1}(0.376) \approx 22^\circ
\]
Common Mistakes in Refraction Calculations
- Forgetting to convert angles to radians for advanced calculations.
- Mixing up the refractive indices for different media.
- Ignoring the critical angle for total internal reflection.
Practice Questions
- A light ray enters glass (\( n = 1.5 \)) from air at \( 45^\circ \). Calculate the angle of refraction.
- Explain the role of refraction in optical fibers.
- Describe one application of Snell’s Law in lens design.
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